What size motor [W] is required to pump 12,000 gallons of water up a water tower (with a height of 25 ft.) in 25 minutes? The density of water is 1,000 kg/cubic meter.
Convert gallons/min to kg/second.
Then multiply the kg/s pumping rate by g*(height). That will equal the rate potential energy is added to the water, in watts.
You should do the calculation.
To find the required motor power, you need to determine the work done by the motor to pump the water up to the water tower.
The work done can be calculated using the formula:
Work = Force × Distance
In this case, the force required to pump the water is the weight of the water being lifted. The weight can be determined using the formula:
Weight = Mass × Gravity
The mass of water can be calculated by converting the volume of water from gallons to cubic meters, and then multiplying it by the density of water.
Now, let's break it down step-by-step:
Step 1: Convert gallons to cubic meters
To convert gallons to cubic meters, use the conversion factor: 1 gallon = 0.00378541 cubic meters
12,000 gallons × 0.00378541 cubic meters/gallon = 45.42492 cubic meters
Step 2: Calculate the weight of water
The weight of water can be calculated using the formula:
Weight = Mass × Gravity
Where:
Mass = Volume × Density
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Weight = (Volume × Density) × Gravity
Weight = 45.42492 cubic meters × 1,000 kg/cubic meter × 9.8 m/s^2
Weight = 446,542.2496 kg·m^2/s^2
Step 3: Calculate the work done
The work done is given by the formula: Work = Force × Distance
In this case, the distance is the height the water needs to be lifted, which is 25 ft. To convert feet to meters, use the conversion factor: 1 ft = 0.3048 meters
Distance = 25 ft × 0.3048 meters/ft
Distance = 7.62 meters
To find the force, we'll use the weight of the water:
Force = Weight
Work = Force × Distance
Work = 446,542.2496 kg·m^2/s^2 × 7.62 meters
Work = 3,399,237.1472 kg·m^2/s^2
Step 4: Calculate motor power
Power = Work / Time
To convert minutes to seconds, use the conversion factor: 1 minute = 60 seconds
Time = 25 minutes × 60 seconds/minute
Time = 1500 seconds
Power = 3,399,237.1472 kg·m^2/s^2 / 1500 seconds
Power ≈ 2,266.16 W
Therefore, a motor with a power of about 2,266.16 Watts would be required to pump 12,000 gallons of water up a water tower with a height of 25 ft. in 25 minutes.